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Cohomology in algebra, geometry, physics and statistics

usually takes place every Wednesday Institute of Mathematics of ASCR, Žitná 25, Praha 1
Chair: Anton Galaev, Roman Golovko, Igor Khavkine, Alexei Kotov, Hong Van Le and Petr Somberg

In this seminar we shall discuss topics concerning constructions and applications of cohomology theory in algebra, geometry, physics and statistics. In particular we shall discuss in first four seminars the relations between vertex algebras and foliations on manifolds, Gelfand-Fuks cohomology on singular spaces, cohomology of homotopy Lie algebras. The expositions should be accessible for all participants.

Contact Geometry of Hydrodynamic Integrability (will be cancelled because of open door days)

Artur Sergyeyev
University of Opava
Wednesday, 7. November 2018 - 11:30 to 12:30
in IM building, ground floor

The search for integrable partial differential systems in four independent variables (4D) is a longstanding problem in mathematical physics. In the present talk we address this problem by introducing a new construction for integrable 4D systems which are dispersionless (a.k.a. hydrodynamic-type) using nonisospectral Lax pairs that involve contact vector fields. In particular, we show that there is significantly more integrable 4D systems than it appeared before, as the construction in question produces new large classes of integrable 4D systems with Lax pairs which are polynomial and rational in the spectral parameter. For further details please see A. Sergyeyev, New integrable (3+1)-dimensional systems and contact geometry, Lett. Math. Phys. 108 (2018), no. 2, 359-376,

Applications of complexes of differential operators in gauge theories

Igor Khavkine
Wednesday, 31. October 2018 - 11:30 to 12:30
in IM building, ground floor
In mathematical physics, gauge theories are variational PDEs that have gauge symmetries (symmetries locally parametrized by arbitrary functions). Generators of gauge symmetries naturally fit into certain complexes of differential operators. I will discuss the structure of these complexes and the possible roles played by their cohomology.

Lie-infinity structures as dg manifolds

<span style="font-family:tahoma,sans-serif; font-size:13.3333px">Alexei Kotov</span>
University of Hradec Králové
Wednesday, 24. October 2018 - 12:15 to 13:00
in IM building, ground floor
<span style="background-color:rgb(255, 255, 255); color:rgb(51, 51, 51); font-family:monospace; font-size:12px">A short intro into Lie-infinity structures via&nbsp;</span><br /> <span style="background-color:rgb(255, 255, 255); color:rgb(51, 51, 51); font-family:monospace; font-size:12px">supergeometry with examples.</span>

Algebraic geometry and number theory applications of vertex operator algebras

Alexander Zuevsky
Institute of Mathematics, Czech Academy of Sciences, Praha&nbsp;
Wednesday, 24. October 2018 - 11:30 to 12:15
in IM building, ground floor
We continue our series of lectures concerning vertex operator algebras and their applications in&nbsp;algebraic geometry and number theory. In particular, we consider a construction and properties of characters for vertex operator algebras on Riemann surfaces.